Question

"У трикутнику АВС відомо , що кут С=90 градусів,ВС=5см,АВ=10см.Знайдіть кут А цього трикутника"

Answer 1

Sin A = BC/AB=5/10=1/2 

За таблицею sin 1/2 = 30градусів

Відповідь: 30 градусів.

Answer 2

Finding the Angle A in Triangle ABC

To find the angle A in triangle ABC, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle C is given as 90 degrees, we can subtract angles B and C from 180 to find angle A.

Let's calculate it step by step:

1. Start with the sum of the angles in triangle ABC: angle A + angle B + angle C = 180 degrees.

2. Substitute the given values: angle A + angle B + 90 degrees = 180 degrees.

3. Rearrange the equation to solve for angle A: angle A = 180 degrees - angle B - 90 degrees.

Now, we need to find angle B. We can use the Law of Cosines to calculate it.

The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we know that side AB is 10 cm and side BC is 5 cm. We can substitute these values into the equation and solve for angle B.

Let's calculate it step by step:

1. Substitute the known values into the Law of Cosines equation: 5^2 = 10^2 + b^2 - 2 * 10 * b * cos(90 degrees).

2. Simplify the equation: 25 = 100 + b^2 - 20b * cos(90 degrees).

3. Simplify further: 25 = 100 + b^2.

4. Rearrange the equation to solve for b: b^2 = 25 - 100.

5. Calculate b: b = sqrt(25 - 100) = sqrt(-75). Since the square root of a negative number is not defined in the real number system, we cannot find the exact value of angle B using the given information.

Therefore, we cannot determine the exact value of angle A in triangle ABC with the given information.